The C(X)-algebra of a net and index theory

Abstract

Given a connected and locally compact Hausdorff space X with a good base K we assign, in a functorial way, a C(X)-algebra to any precosheaf of C*-algebras A defined over K. Afterwards we consider the representation theory and the Kasparov K-homology of A, and interpret them in terms, respectively, of the representation theory and the K-homology of the associated C(X)-algebra. When A is an observable net over the spacetime X in the sense of algebraic quantum field theory, this yields a geometric description of the recently discovered representations affected by the topology of X.

A section with applications to subtrivial C*-bundles and quantum field theory has been added. To appear on Journal of Functional Analysis

References in corpus (3)

• Quantum charges and spacetime topology: The emergence of new superselection sectors
• The K-homology of nets of C*-algebras
• Representations of nets of C*-algebras over S^1

Cited by in corpus (5)

• The K-homology of nets of C*-algebras
• Locally $C^{\ast }$ Algebras, $C^{\ast }$ Bundles and Noncommutative Spaces
• Background potentials and superselection sectors
• Aharonov-Bohm superselection sectors
• Loop groups and noncommutative geometry